Surfaces such as the exterior of the earth are modeled by producing three-dimensional data for the surface, which includes a z-axis value falling within a particular contour level for each x, y coordinate of the surface in a Cartesian plane. The coordinates of the surface that have a common z-axis value form a contour level that may be defined by a polygon or other shape. The contour levels defined by the shapes may be used to produce contour maps or for other purposes such as volumetric calculations. Such contours, contour maps, and related calculations are often useful in the petroleum industry where knowledge of the earth's surface and local volume is necessary to efficiently find and extract oil reserves.
The z-axis data that define the contour levels for the surface being modeled may be generated in various ways, but inevitably, there are z-axis values that are null such that the contour level for a given x, y coordinate or set of x, y coordinates is undefined. For example, z-axis data may stop along an edge of the area being modeled even though the contour level at the edge might otherwise continue had a larger area been included in the modeling. Additionally, z-axis data within the modeled space may be null as well such as due to imperfect data gathering.
The null values for the z-axis present in a surface model result in difficulty. The null values result in a contour being left open because the polygon or other shape resulting from tracing the bounds of the contour cannot return to its starting point due to a break in the continuity of the z-axis data. When the contour is left open, the ability to compute values such as the area of a contour or the volume of the surface being modeled is complicated. Furthermore, rendering a display of a colorfilled contour map is also complicated by open contours. For example, one previous solution required that the contours be dissected by grid cell of the surface model, that a polygonal net be built on each cell, and then the colorfill polygons be extracted from the net and displayed.
The display of a colorfilled contour map is also complicated, even for closed contours, by the use of opaque colors for the various contour levels. When contours are being displayed as a colorfilled contour map, the display of one polygon or other shape representing one contour level will overlap with the display of another polygon or other shape representing a different contour level. Thus, the portions of contours that are obscured by overlapping contours but that should not be obscured in the display must be corrected to result in an accurate contour map display.